Uncertainty of Porosity-Permeability Relationships from REV-scale Numerical Fluid Simulations

Abstract

Empirical porosity-permeability and grain size-permeability relationships have long been used and researched. However, they often under- or overestimate permeability because they simplify complex micro scale porous medium descriptions, such as tortuosity or pore size distribution, into nondescript parameters or constants. This paper aims to highlight the large range of possible permeability values that can be obtained from identical porosity and grain size distributions, but describe different pore scale porous media. To achieve this, numerical flow simulations were performed on irregular grained and circular grained porous media which contain identical grains and porosity but vary in spatial distribution of the grains within the domain. Subsequently, the domain was analyzed in terms of representative elementary volume, pore size distribution, grain size distribution, quantitative grain morphological parameters, porosity, and permeability. The results were compared to five well known empirical relationships: Hazen (1892), Slichter (1898), Beyer (1964), Kozeny-Carman (1953), and Barr (2001). Results showed a linear relationship between permeability on a logarithmic scale and porosity on an arithmetic scale with uncertainty increasing as porosity increased. Porous media containing equally sized circular grains as irregular grains in terms of sieve radius showed higher permeability values. Empirical relationships correctly captured the impact of porosity on permeability, but were unable to yield correct values, and even deviated by over a factor 10 for some porous media. This study emphasizes the need for more extensive research into pore scale processes influencing permeability and provides ideas for future research.